Many different types of packaging containers are known. Some have a two-piece construction, in which a molded base or tray has a recessed portion defining a product-receiving cavity and a lidding film attaches to the tray to cover the cavity and seal the contents of the tray. Such containers are commonly seen in restaurants and cafes to hold unit servings of food products such as jelly, honey, and butter. The lidding film seals to a flange portion of the tray that surrounds the cavity. To facilitate initially separating the lidding film from the tray, the tray is scored at one corner of the flange to define a small frangible corner piece. When opening the package, the user grasps the corner piece and the portion of the lidding film attached to it, and breaks the corner piece off of the remainder of the tray. The user then peels the lidding film apart from the flange with a smooth pulling motion while still grasping the small corner piece and the corresponding corner of the lidding film. During this procedure the lidding film appears to remain intact with no rips or tears, and the small corner piece of the tray remains attached to the lidding film.